Method for the automatic calibration-only, or calibration and qualification simultaneously of a non-contact probe

ABSTRACT

The present invention relates to a method for calibrating a non-contact probe on a localizer. The present invention further relates to a method for the simultaneous calibration and qualification of a non-contact probe on a localizer. Both methods do not require user intervention, and use a single artifact.

CROSS REFERENCE TO RELATED APPLICATION

This application claims priority to U.S. Provisional Patent Application60/379,592 entitled “METHOD FOR SELF-CALIBRATION OF A NON-CONTACT PROBE”and filed on May 8, 2002. The disclosure of the above-described filedapplication is hereby incorporated by reference in its entirety.

FIELD OF THE INVENTION

The present invention relates to a method for a non-contact probecalibration on a localizer. The present invention further relates to amethod for the calibration and qualification of a non-contact probe on alocalizer in a single step procedure, using a single reference object,also referred to as an artifact.

BACKGROUND OF THE INVENTION

Generally a non-contact probe comprises of one or more emitter sourcesand one or more receivers. An emitter source projects waves, for examplelight waves, on the object of interest; the receiver(s) comprising forexample a camera, capture(s) the returning waves from the object. Forinstance, if the receiver is a CCD-camera, it will take one or moreshots of the object. By moving the object relative to the non-contactprobe or vice versa, shots of the complete object can be taken, i.e. theobject is being scanned. Each shot represents a one-dimensional (1D),two-dimensional (2D) or three-dimensional (3D) projection of the objectdepending on the physical form and working principle of the receiver(s).To obtain accurate 3D points on the surface of the object, relative to afixed coordinate system, from multiple shots the following systemparameters are preferably required:

-   -   1. the 3D position of the emitter source(s) relative to the        receiver(s);    -   2. the 3D position and orientation of the emitted waves,        relative to the receiver(s), coming from the emitter source(s);    -   3. the characteristics such as focal point of lenses of the        receivers used in the non-contact probe;    -   4. the dimensions and measuring resolution of the receiver(s);        and    -   5. the 3D position and orientation of the non-contact probe or        the object relative to a fixed coordinate system, for each        receiver capture.

The actual values of the parameters 1 to 4 are calculated during thecalibration. Some of the actual values of parameter 5 are calculatedduring the qualification procedure, others are given values readilyobtainable from the object-non-contact probe, set-up. When theseparameters are calculated for the given non-contact probe, theconversion, also called compensation, from receiver readings to accurate3D points can be performed.

To be able to move the non-contact probe relative to the object, theprobe is mounted on a localizer. This localizer can be a structure,portable or non-portable, on which the probe is mounted, like forexample a tripod. This localizer can also be structure with moving axes,motorized or non-motorized, where the probe is mounted on the end ofsaid axes, dependent to all other axes, like for example a robot, amilling machine or coordinate measuring machine (CMM). These last typesof localizer can have the possibility to record the position and/or therotation of the probe.

Some of the state-of-the-art techniques actually calculate parameters 1to 5 explicitly using dedicated measurements in a sequential manner.Adjusting these parameters is difficult because of their complexinteractions and adjustment can be time consuming.

Other state-of-the-art techniques for calibration and qualification donot calculate these parameters explicitly. In the first step, thereceiver readings are first transformed in one, two or three dimensions,depending on whether the receiver itself is capable of measuring one,two or three dimensions. In this calibration step a receiver reading inreceiver units is transformed to a point in e.g. SI units. Thecalibration can take several phenomena into account; for example,correcting the perspective since the object is not always parallel tothe receiver or scaling correctly the readings. Finally, it must modelcorrectly systematic reading errors in the receiver(s)—which is acomplex operation.

The second step, the qualification, consists of determining the accurateposition and orientation of the non-contact probe relative to a fixedcoordinate system. The qualification procedure is generally performed bythe end-user using special artifacts or other measuring equipment. Thequalification procedure often requires an essential manual alignment ofthe artifact/measuring equipment with the non-contact probe.

Both steps, calibration and qualification, are based on some parametersthat are tuned or optimized to obtain the 3D points accurately. Allstate of the art algorithms determine the values of the parameters forthe two steps separately, usually scanning different artifacts withknown features, dimensions, etc.

Although, it is easier to obtain few parameters at a time, thistechnique suffers from major drawbacks.

The various parameters have complex interactions and it is extremelydifficult, if not impossible, to predict the effect of an individualparameter. Hence, an error at the very start can propagate and producefaulty results in the determination of the subsequent parameters.Unfortunately, there is as yet no correct method to back-propagate theinformation. As a result, even with the utmost care, the parameterfitting will be sub-optimal in the sense that the accuracy of thethree-dimensional points will not be the best.

Another drawback of the de-coupled procedure is that it requires manyhigh-level user interactions, which is time consuming and unreliable.

As a consequence, these techniques for calibration and qualificationcannot be performed at the user's site, nor by the user itself.

To overcome these problems, the present invention provides a novelintegrated approach using one single artifact. The present inventionprovides a novel method that computes all probe parameters in one singlestep using only one artifact. In this approach, a general functionconverts directly a receiver reading into a three dimensional point.This function corresponds to a sequence of calibration and qualificationand therefore, depends on many parameters similar to the ones used inthe classical de-coupled technique.

However, by expressing the conversion with one function, allinteractions between the parameters are considered. Also, if the objectbeing measured is known, the influence of a single parameter candirectly be measured in terms of accuracy of the resulting 3D point.

The present invention provides a method to scan a known reference objectand to use this information to find the values of the parameters thatgive the most accurate points. A single requirement of this method isthe knowledge of the class of the reference object, like sphere or cube,box the actual sizes, aspect ratio, etc and a volume scan of the object.With these data, the entire procedure, calibration, and qualification isperformed automatically.

SUMMARY OF CERTAIN INVENTIVE ASPECTS

One embodiment of the invention is a method for the calibration only, orcalibration and qualification simultaneously of a point cloud generator,said point cloud generator comprising a non-contact probe and alocalizer, comprising determining the transformation of an electricalreading of the receivers in said non-contact probe in point coordinatesrelative to the said probe and, if calibrating and qualifyingsimultaneously, also determining the orientation of the said non-contactprobe in the measuring volume of the said localizer, either method usinga single artifact.

Another embodiment of the invention is a method as described above,whereby said artifact is a physical object susceptible to point cloudgeneration, whose outer shape and/or part thereof is definable using amathematical function and/or look-up tables.

Another embodiment of the invention is a method as described above,whereby said artifact is a sphere, cylinder or box.

Another embodiment of the invention is a method as described above,whereby said artifact is a sphere of unknown diameter.

Another embodiment of the invention is a method as described above,whereby said artifact has unknown dimensions prior to the execution ofsaid method.

Another embodiment of the invention is a method as described above,whereby said artifact has unknown position with respect to saidlocalizer prior to the execution of said method.

Another embodiment of the invention is a method as described above,whereby said method is performed without manual intervention.

Another embodiment of the invention is a method as described above,whereby said method is executed at a user's site.

Another embodiment of the invention is a method as described abovecomprising the steps of:

a) scanning said artifact using said point cloud generator,

b) calculating cloud points, P, using parameters relating to calibrationand qualification,

c) calculating the position and optionally the orientation and/or sizeof said artifact using P calculated in step b) and knowledge of theartifact according to a mathematical function and/or look-up tableswhich define said artifact,

d) comparing the values of P, with those calculated for the artifactderived from step c),

e) adjusting parameters relating to calibration and qualification, andf) repeating steps b) to e) until parameters relating to calibration andqualification are obtained which provides the closest comparisonaccording to step d).

Another embodiment of the invention is a method as described abovewhereby step b) is based on the generic function [1]P=Q(f(Pr))+m(Pr)  [1]

where

-   -   Pr is a reading of a receiver of the non-contact probe,    -   P is a cloud point, calculated from Pr, relative to a fixed        coordinate system,    -   f is a general mapping function, that maps receiver readings to        1D, 2D or 3D point coordinates, relative to a coordinate frame        fixed to the non-contact probe, and    -   Q is the orientation of the non-contact probe and m(Pr) is the        position of said probe for a given value of Pr, both values with        respect to a fixed coordinate frame; none or either values        considered as known and fixed parameters.

Another embodiment of the invention is a method as described abovewherein f is a non-uniform rational B-spline function.

Another embodiment of the invention is a method as described above,wherein steps b) to f) comprise:

-   -   b) calculating points according to function [1], said function        re-expressed as:        P=F(Pr, S)  [2]        -   wherein Pr is a reading of a receiver of the non-contact            probe,        -   P is a point, calculated from Pr, relative to a fixed            coordinate system,        -   F is a compensation function based on f, Q and m(Pr), said            compensation function being applied to Pr using parameter            set S,    -   c) calculating the position and optionally the orientation        and/or size of said artifact using values of P obtained in step        b),    -   d) comparing the values of P, with those calculated for the        artifact derived from step c),    -   e) adjusting S, and    -   f) repeating steps b) to e) until value of S is obtained which        provides the closest comparison according to step d).

Another embodiment of the invention is a method as described abovewherein the values calculated for the artifact as mentioned in step d)are derived from a mathematical function and/or look-up tables whichdefine said artifact, the values corresponding to the position, and ifcalculated orientation and/or size as obtained in step c).

Another embodiment of the invention is a method as described abovewherein step c) comprises:

-   -   g) comparing the points P obtained in step b) to those expected        of said artifact according to a mathematical function and/or        look-up tables which define said artifact,    -   h) adjusting one or more of the values corresponding to the        position and optionally the orientation and/or size of said        artifact, and    -   i) repeating steps g) and h) until values corresponding to the        position, and if calculated orientation and/or size are obtained        which provide the closest comparison according to step g).

Another embodiment of the invention is a method as described above,wherein the comparison performed in step d) comprises one or moreaverage square distance, variance, volume, area, and/or axis of inertiacalculations.

Another embodiment of the invention is a method as described above,wherein the comparison performed in step d) comprises one or moreaverage square distance, variance, volume, area and/or axis of inertiacalculations.

Another embodiment of the invention is a method for the simultaneouscalibration and qualification of a point cloud generator, said pointcloud generator comprising a two-dimensional line laser scanner mountedon a 2D co-ordinate measuring machine, comprising:

-   -   a) scanning a sphere using said point cloud generator,    -   b) calculating points according to function [2]        P=F(Pr, S)  [2]        -   wherein Pr is a reading of a receiver of the two-dimensional            line laser scanner,        -   P is a point, calculated from Pr, relative to a fixed            coordinate system,        -   F is a compensation function based on f, Q and m or m(Pr),            said compensation function being applied to Pr using            parameter set S,        -   Q is the orientation of the non-contact probe; m(Pr) is the            position of said probe for a given value of Pr, both values            with respect to a fixed coordinate frame and none, either or            both values considered as known parameters,    -   c) comparing the points P obtained in step k) to those expected        of said sphere according to a mathematical function defining        said sphere,    -   d) adjusting one or more of the values corresponding to the        position and size of said sphere,    -   e) repeating steps c) and d) until values corresponding to the        position and size are obtained which provide the closest        comparison according to step c),    -   f) comparing the values of P, with those calculated for the        sphere, the latter obtained from mathematical function which        defines said sphere, and the values corresponding to its        position and size as obtained in step e).    -   g) adjusting S,    -   h) repeating steps b) to e) until value of S is obtained which        provides the closest comparison according to step f).

Another embodiment of the invention is a method to allow an unskilledoperator to perform a calibration only, or calibration and qualificationsimultaneously of a point cloud generator, using a method as describedabove.

Another embodiment of the invention is a method for performing acalibration only, or calibration and qualification simultaneously of apoint cloud generator within 5 minutes of generating the cloud point,using a method as described above.

Another embodiment of the invention is a method for performing acalibration only, or calibration and qualification simultaneously of apoint cloud generator without manual intervention, using a method asdescribed above.

Another embodiment of the invention is a use of a single artifact forperforming the calibration only, or calibration and qualificationsimultaneously a point cloud generator according to the method asdescribed above.

Another embodiment of the invention is a computer program wherein amethod as described above is performed.

Another embodiment of the invention is a computer having a computerreadable medium adapted and programmed to carry out the computer programas described above.

Another embodiment of the invention is a non-contact probe usableaccording to the method as described above.

Another embodiment of the invention is a non-contact device comprisingan artifact and a non-contact probe as described above mounted on alocalizer.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram of a point cloud generator.

FIG. 2 is a flowchart illustrating one embodiment of a method ofcalibration only, or calibration and qualification simultaneously of apoint cloud generator.

DETAILED DESCRIPTION OF CERTAIN INVENTIVE EMBODIMENTS

A “non-contact probe” can be defined as any device mounted on alocalizer that through non-contact sensing conducts 1D (distance), 2D or3D coordinate measurements.

A “localizer” can be defined as any system positioning and orientating anon-contact probe in space, that returns the position and/or theorientation of the non-contact probe in 1D-, 2D- or 3D coordinates.

A “receiver”, can be an electronic device in the non-contact probe thatcaptures the waves coming from the object to be measured, resulting inone or multiple electrical readings. Most of the time these electricalreadings are voltage readings on pixels of a CCD-camera.

An “artifact” can be any physical object susceptible to point cloudgeneration, whose outer shape and/or part thereof is definable using amathematical function and/or look-up tables. Said artifact may be, forexample, a sphere, cylinder, cube or box, two spheres joined together, adumb-bell, a sphere joined to a cube etc. Said artifact may also be anyirregular shape such as a mobile phone, a pen, a calculator etc. Themethod of obtaining a mathematical function and/or look-up table thereofis known to the skilled artisan. Depending on the geometry of theobject, its dimensions may be known with accuracy; alternatively thedimension may not be accuracy known, or not known at all.

A “look-up table” can be a data list that defines the shape anddimensions of the object.

A non-contact probe generally comprises of one or more emittersource(s), sending (e.g. light) waves to the object of interest, and oneor more receivers, which capture the part of the object that is “hit” bythe emitter source. The conversion of the electrical readings of thereceiver to an accurate 3D point requires the steps of calibration andqualification executed on beforehand.

A “point cloud generator” 10 can be a system that comprises twocomponents, namely a non-contact probe 12 and a localizer 14, asillustrated in FIG. 1, whereby both components can be used for 1D, 2D or3D position and/or orientation measurements.

“Calibration” can be the procedure to identify the conversion betweenthe electrical reading of the receiver in the non-contact probe and 1D,2D or 3D point coordinates in SI units. In other words, calibration isthe procedure to transform an electrical reading in accurate pointcoordinates. These point coordinates are calculated relative to acoordinate system connected to the non-contact probe.

“Qualification” can be defined as a procedure of completely andaccurately identifying the position and orientation of the non-contactprobe in the measuring volume of the localizer, possibly usinginformation readily made available by the localizer itself. Thisprocedure is to be performed each time the non-contact probe is mountedon the localizer or each time its position or orientation with respectto the localizer is changed. Thus, qualification is the procedurewhereby the position and the orientation of the coordinate systemassociated with the non-contact probe is defined with respect to a fixedcoordinate system.

Finally, “compensation” can be defined as a procedure of making theconversion between the electrical reading of a receiver in thenon-contact probe and 1D, 2D or 3D point coordinates using thecalculated parameters of the calibration and qualification.

The calibration and qualification steps depend on a variety ofparameters, which up to now were determined individually using differentartifacts. An “artifact” is used as synonym for a “reference object” andis defined as above.

The present invention relates to a calibration method that determinesall the parameters of a non-contact probe mounted on a localizer usingonly one artifact and the localizer.

One aspect the present invention allows the entire calibration andqualification procedure to be carried out in one single step using onlyone artifact. Hence the calibration and qualification procedure can beautomated with little input from the end-user. In addition, this singlestep operation provides a more accurate determination of the parameters,which results in a more accurate activity of the non-contact probe.

In one embodiment, the present invention relates to a method for thecalibration of a non-contact probe mounted on a localizer whereby thelocalizer is used to calibrate the probe. Thus, the present inventionrelates to a method for the calibration of a point cloud generator, saidpoint cloud generator consisting of a non-contact probe and a localizer,comprising determining the transformation of an electrical reading ofthe receivers in said non-contact probe in point coordinates relative tosaid probe using said localizer.

State-of-the-art techniques presently perform the calibration of thenon-contact probe, dismounted from the localizer, on a separate,dedicated device, mostly in well-defined metrology room conditions.

In contrast, the method according to the invention is performedautomatically, without manual intervention, and preferably said methodis executed at a user's site.

In a further embodiment, the present invention relates to a calibrationmethod according to the invention whereby the said method is executed ona single artifact. Said artifact is as defined above.

Furthermore, the present invention relates to a method for thecalibration and qualification of a non-contact probe whereby both stepsare performed simultaneously. Therefore, in another embodiment, thepresent invention relates to a method for the calibration andqualification of a non-contact probe comprising determining thetransformation of an electrical reading of the receivers in saidnon-contact probe in point coordinates relative to the said probe andidentifying the position and orientation of the said non-contact probein the measuring volume of the said localizer, thereby determiningcalibration and qualification parameters simultaneously.

The former technologies of non-contact probes perform the calibrationand the qualification in two different steps. The present inventionconsists of a one step procedure for calibration and qualification. Byusing the same measurements of the non-contact probe mounted on thelocalizer on only a simple artifact, the non-contact probe is calibratedand qualified. This novel method is characterized by some majorimprovements compared to the state-of-the-art technologies. The samemeasurement procedure can be followed for calibration and qualification.Furthermore, calibration and qualification are performed in a singlestep. The calibration can be conducted by the end-user, where previouslythe calibration procedure was performed in the factory during productionof the non-contact probe or at the end-users location by theservice-engineers of the manufacturer. Therefore, the present methodrepresents not only an easier but also a more time-effective method.

In a further embodiment, the present invention relates to a method forthe calibration and qualification of a non-contact probe wherebycalculation of the calibration and qualification parameters is performedon the same artifact. In a one embodiment, said artifact consists of oneor more spheres, cylinders, cubes or boxes, any regular or irregularphysical object. According to the present invention the entirecalibration-qualification procedure can thus be totally automated; inother words there is a little or no manual interference and saidprocedure does not rely upon the skill of the operator. Furthermore,calibration and qualification can be performed at the user's site.

As mentioned, the calibration and qualification steps of a non-contactprobe depend on a variety of parameters. In another embodiment, thepresent invention relates to a method for determining the parameters ofa non-contact probe in a single step using a single artifact.

The present invention is based on a general mapping function thatdirectly converts a receiver reading into a 3D point. This functiondepends on various parameters that need to be numerically determined. Inthe following description, the general mapping function according to theinvention is described with use of the conventional division incalibration and qualification. However, it is the aim of the inventionto provide an approach that mixes these two steps in one singlefunction. According to the invention, a single measurement procedure toestablish the parameters has a greater accuracy than establishing theset of parameters in separated methods.

1. Calibration

The calibration step consists essentially of a mapping from the receiverreadings to a 1D, 2D or 3D point relative to a coordinate systemconnected with the non-contact probe. The dimensions of the point areequal to the dimensions of the receiver. For example a camera with asquare CCD-array will produce two-dimensional points after calibration.The goal of the calibration is to express the one-, two- orthree-dimensional coordinates of a point in terms of its receiverreadings.

The “mapping” provides a description of this correspondence. It consistsof a function that maps a reading from the receiver domain of allreadings to a 1D, 2D or 3D point. Ideally, the mapping function shouldbe able to model various physical effects of the non-contact probe suchas the perspective, imperfectness of working principle or heterogeneousreading resolution and sensitivity.

Several methods have already been proposed in the literature that definegeneric or specialized mapping functions. The simplest method consistsof defining one single function that covers the entire mapping area. Theform of this function is critical and prior knowledge of the problem isnecessary to make an educated choice. The second class of mappingmethods is generic; it is able to effectively model any mapping functionprovided that the number of parameters is sufficiently high. Thesemethods work by a divide-and-conquer approach, dividing the mapping areain smaller area and defining simple shape functions for the localmapping. The local mapping is then aggregated into a global mapping.

In the present invention any general mapping function can be used, aslong as the function offers enough detail to model an accurateconversion from reading to point. For the sake of generality, all pointshere are considered to be three dimensional. One or two dimensionalpoint can be represented by a three dimensional point without any lossof information. The general representation is given below where P_(r)(resp. P_(3D) ^(c)) represents the receiver reading (resp. 3D point), ƒis the general mapping functionP _(3D) ^(c) =f(P _(r)),  (1)With ƒ defined asf:D->

^(3.)  (2)and

, the three dimensional space and D, the domain of the all possiblereadings of all receivers: D=∪_(∀i)D_(i)  (3)D_(i)∩D_(j)=Øfor i≠j  (4)D_(i), the domain of all possible readings of the i^(th) receiver andthis for all receivers.

A crucial question concerns the amount of data needed to compute theactual parameters of the mapping function. Unfortunately, there is nodefinite answer to this question. It depends on the accuracy needed andon the scale of the phenomenon studied.

2. Qualification

Qualification consists of a three-dimensional mapping. The calibrationmaps the reading onto a point located in the physical space, relative toa coordinate system fixed to the non-contact probe. The exact positionof this non-contact probe and the determination of its orientation arethe tasks of the qualification. The position and the orientation will bedetermined relative to a coordinate system fixed to the object to bescanned.

The non-contact probe coordinate system is described by 6 parameters,three translation components and three rotation components. The systemcan be decoupled into the translation component m of the non-contactprobe and in the rotation matrix Q. A three-dimensional point P_(3D)^(q) relative to the fixed coordinate system is written asP _(3D) ^(q) =QP _(3D) ^(c) +m,  (5)with P_(3D) ^(c) a three-dimensional point relative to the non-contactprobe coordinate system.

In instances where the value of m depends on Pr, the equation may berewrittten as Equation 5.1, which also cover instances when m isindependent of Pr.P _(3D) ^(q) =QP _(3D) ^(c) +m(Pr),  (5.1)Where m(Pr) is the value of m when m depends on Pr.

In general as the localizer moves the non-contact probe and/or theobject in space the relative position and orientation of the probe tothe object changes. In other words the rotation matrix Q and translationcomponent m both change during movement. Dependent on the type oflocalizer, a CMM or robot, some of the components of Q and m areconstant and/or known during the movement of the probe and the object.The use of these types of localizers is within the scope of theinvention. For example, a CMM might produce the position of the probeand the object during movement with a good accuracy. In this case thecomponent m is considered to be known and does not need to be identifiedduring the qualification.

As described above, the necessary steps to convert individual readingsof the receivers into actual three-dimensional coordinates, with (ifavailable) the knowledge of the position and orientation of the probegiven by the localizer at discrete time steps, were de-coupled. Byaggregating these various steps, we can thus express directly a 3D pointP_(3D) ^(q) (also known as P herein) in terms of a receiver readingP_(r) byP _(3D) ^(q) =Q(f(P _(r)))+m,  (6)orP _(3D) ^(q) =Q(f(P _(r)))+m(P _(r)),  (6.1)where ƒ is the calibration function, Q, m and m(Pr) are the position andorientation of the probe stemming from the qualification. Thesefunctions and these symbols have been defined in eqs (1) to (5.1).

Equations (6) and (6.1) contain the following parameters to be definedin the calibration-qualification procedure:

-   -   the function ƒ is a general mapping function with enough        parameters to accurately model the transformation from receiver        reading to 3D point in the probe space. Such functions are known        in the art. If for example a polynomial function is chosen as        mapping function, then the parameters are the coefficients. The        degree and the type of polynomial are not parameters but        constants.    -   Depending on the accurate information obtained from the        localizer, either three translation components (the position m),        or three rotations (the orientation Q), or both are considered        as parameters. For example if the localizer is a CMM with        accurate information on the position of the probe in the        localizer space and the probe performs only parallel movements,        the three rotations (the orientation Q) are the only parameters.

All these parameters can be grouped in a parameter set S and theequation (6) can be rewritten as:P _(3D) ^(q) =F(P _(r) ,S)  (7)With F the compensation function based on a calibration—qualificationprocedure with parameter set S:F:D->

³   (8)And D defined as in eqs. (3) and (4).

In another embodiment, the present invention relates to a method ofdetermining calibration and qualification parameters, which is based ona generic function, said generic function being a non-uniform rationalB-spline function. The present invention relates to a new generalprocedure or method for determining all these parameters in a singlestep. In an embodiment the present invention relates to a method ofdetermining a parameter configuration comprising the steps of:

-   -   scanning an single artifact; and    -   applying a computational procedure to adjust all said parameters        directly and simultaneously using the scanning data.

Said parameter configuration comprises the parameters mentioned abovewhich are required to establish a generic model in which the steps ofcalibration and qualification are integrated.

In one embodiment of the invention, the artifact used for calibration,qualification and position interpolation of the non-contact probe isidentical to the artifact used for the qualification of probe which is atactile or contact probe and said artifact is a sphere.

The method of the invention for simultaneous determination ofcalibration and qualification using a single artifact has several keyfeatures. Importantly, only one single artifact is used. Also, the exactsize, position, or orientation of this artifact is not initially known.Furthermore, all parameters are evaluated concurrently. In addition, themethod performs only one scan of the reference object or artifact andvery little user interaction is required. Using this method the adjustedparameters are obtained, which can be used in the above-describedgeneric function.

In a preferred embodiment, the present invention relates to a method ofdetermining calibration and qualification parameters comprising thesteps of

-   -   scanning a single artifact;    -   determining the optimal position, and optionally, the        orientation and/or size of said artifact using the scanning        data;    -   evaluating the quality of said parameter configuration via a        multidimensional optimization procedure; and    -   determining the best configuration of the parameters.

An example of the procedure is described in more detail as follows: Aninitial parameter configuration S in equation (7) is chosen. Thisconfiguration is used to establish the generic model described above.Subsequently, an artifact is scanned. The data obtained by a scan ofthis reference object is a series of receiver readings optionallytogether with the positions and/or orientations of the probe relative tothe artifact. When applying the generic model, which was establishedusing the configuration S, to this series of receiver readings a cloudof 3D points is obtained. As neither the exact position, orientation norsize of the reference object are known, using the cloud of 3D points theoptimal position and optionally the orientation and/or size of theartifact that matches the 3D points is first determined. Note thatcalculating the optimal orientation or size of an artifact is optional,depending on the geometry of the object, and whether any dimensions arealready known; when a sphere is used, for example, the orientation doesnot need to be determined, as described below; when the artifact is anobject of known dimensions, only the position and orientation of theobject need to be determined. Once the position, orientation and size ofthe artifact have been determined, the cloud of 3D points can be“compared” with the scanned artifact, and then the quality of theparameter configuration (S) is evaluated. Finally, since a cost or aquality can be assigned to each configuration S, a standardmultidimensional optimization procedure can be applied to determine thebest configuration S_(best).

In the following description, the standard multidimensional optimizationprocedure is explained in further detail. Designing a proper costfunction is crucial in any optimization procedure and it has been thesubject of many publications in the prior art. A “good” cost functionshould represent accurately the model being investigated without beingtoo complex as to prevent any optimization. In other words, a minimum ofthe cost function should represent an optimal configuration of theparameters while plateau's in the cost function should be avoided toensure convergence of the iterative algorithm. From a computationalpoint of view, the cost function should also be easy to compute as itneeds to be evaluated many times.

A multidimensional optimization procedure of the present invention isdisclosed in the following description. In one aspect of the invention,an algorithm starts from an initial configuration S_(ini) and defines itas the current configuration S_(cur). Then, in a loop, the configurationis iteratively adapted, yielding each time a new S_(cur), in an attemptto better match the cloud of 3D points with the artifact shape. Thealgorithms stops when the accuracy can no longer be improved, i.e. whenthe cost function is at its minimum.

In a method of the present invention, the evaluation of the costfunction consists of two phases. The first phase consists of determiningthe best position, and optionally size and/or orientation of an artifactusing the 3D points obtained with the active configuration S_(cur).Depending of the shape of the artifact a direct computation or aniterative computation is performed.

In the second phase, the distance between the individual 3D points andthe artifact are computed and aggregated, using, for example, one ormore average square distance, variance, volume, area computation, axisof inertia calculations, or other method known in the art, to give theactual cost of the parameter configuration. In the ideal situation, whenall distances are zero, i.e. all points lie perfectly on the artifact,the cost function is zero and the active configuration is optimal. Anexample of an algorithm is given below:

-   -   1. Choose an initial configuration S_(ini)    -   2. Set initial configuration as current configuration        S_(cur)=S_(ini)    -   3. Set S_(best)=S_(cur) and the cost C(S_(best))=    -   4. While C(S_(best)) is not within the desired accuracy (as set        by the user), do the following:    -   5. Compute the cloud of 3D points from eq. (7), using the        receiver readings and S_(cur)    -   6. Evaluate the best position, and optionally, orientation        and/or size of the artifact for the computed 3D points    -   7. Compare the virtual artifact with the 3D points to compute        the cost C(S_(cur))    -   8. If C(S_(cur))<C(S_(best)), S_(best)=S_(cur).    -   9. Choose a new S_(cur)

At the end of the computation, the parameters of S_(best) are those thatgive the best representation of the artifact.

Step 6 determines the best position and optionally, the orientationand/or size of the artifact, by comparing a cloud of 3D points generatedin step 5 with the artifact. In one aspect of the invention, if theartifact is an object of unknown position, dimension(s) and orientation,but its shape is mathematically defined, the best-fit position,dimension(s) and orientation may be derived by iterative fitting theunknown position, dimensions and orientation using the mathematicaldescription of the shape to the cloud of 3-D points. In another aspectof the invention, if the artifact is an irregular object of accuratelyknown dimensions, its position and orientation may be determined byiteratively fitting the best position and orientation of the objectdimensions to the cloud of 3D points. The dimensions may be read, forexample, from a look-up table. The method can determine the bestposition, orientation and size of the artifact, for any combination ofavailable object parameters. The iterative fittings of the artifact tothe cloud points may be performed by a shaping-matching model comprisingany known methods of the art. Possible shapes of the artifact includecylinders, cubes, boxes, spheres, any irregular or regular shape.

For the purpose of illustration, general shape matching with a spherewill be described, although the procedure is non-limiting for thepresent invention. A sphere can be described by 3 parameters for itscenter c: (c_(x), c_(y), c_(z)), and one parameter for its radius r. Forevery point p, with parameters (p_(x), p_(y), p_(z)), it is then easy tocompute its distance d to the sphere as

 d=∥p−c∥ ₂ −r=((p _(x) −c _(x))²+(p _(y) −c _(y))²+(p _(z) −c_(z))²)^(1/2) −r  (9)

or a pseudo distanced′=∥p−c∥ ₂ ² −r ²=(p _(x) −c _(x))²+(p _(y) −c _(y))²+(p _(z) −c _(z))²−r ²  (10)For a given set of parameters (c, r), it is then possible to define acost function:C _(art)(c,r)=Ód ²,  (11)orC _(art)(c,r)=Ód′ ²,  (12)where the sum goes over all points of the receiver(s).

Standard derivation techniques can be used to determine the values of cand r that minimize C_(art). When the cost function C_(art) is nonlinear, a regular multidimensional optimization procedure can be used todetermine the best values of c and r.

The results of step 6 is a virtual artifact whose best position, sizeand orientation have been calculated (or were partly already known). Instep 7, the cloud of 3D points generated in step 5 is compared to saidvirtual artifact, and a cost of fitting is generated for a set of Sparameters. The method used to generate the cost (the cost function, C)can be any known in the art, as already mentioned above. The value of Sis adjusted until the cost of fitting is minimized. The minimizationprocedure can be any known in the art.

Thus, the two cost functions C and C_(art) used in thecalibration-qualification procedure are described above. The generalcost function C is used to find the parameter configuration for thecalibration and qualification while the second function C_(art) is usedinside the first to find the best shape.

According to the above example, only the shape of the sphere is neededand not its actual size. As a consequence, the radius r of the sphere isrequired to be determined by the shape-matching model C_(art). Of courseif, for other shapes, additional information is available, such as asize, an aspect ratio, dimensions etc, they can be easily used to reducethe number of parameters required to be determined by the shape-matchingmodel. In the example provided above in which the artifact is a sphere,were the radius to be already known, the problem would be reduced to thedetermination of the optimal sphere center c—and so there would only bethree parameters to determine.

When robust optimization algorithms are used, the initial configurationis of little importance. However, when the cost function contains manylocal minima, providing an initial configuration close to the optimal,but unknown, configuration is desirable. With the model according to thepresent invention, it is also possible to automate this step. Indeed,the model according to the present invention contains two looselyconnected entities, namely, the calibration and the qualification. Inorder to the find an initial good configuration, one of both entities isfixed and the other one is solved.

More precisely, when qualification is not required and hence neglectedin the calculation, only the calibration is investigated. When only acalibration is performed, values of Q and m according to equation 6.1should be known and are fixed in the calculation.

With a fixed calibration, the optimization of, at most, 6 parameters ofthe qualification can be performed in a straightforward manner using amethod of the present invention. When only a qualification is performed,the value of F should be known and fixed in the calculation.

When calibration and qualification calculations are performed separatelyas described in the preceding paragraphs, the values obtained by onecalculation be used as the fixed, known parameter in the othercalculation. For example, a qualification-only optimization will producevalues of Q and m; the values of Q and m so calculated can be used asthe fixed values in the calibration-only optimization. Performingseveral iterations of separate calibration and qualificationcalculations wherein the parameters obtained from one calculation areused in the other calculation, results in an initial configurationparameter set that is close to the optimal configuration achieved byperforming calibration and qualification simultaneously.

The method presented herein allows an unskilled operator to perform asimultaneous calibration and qualification of a point cloud generator.The quality of said calibration and qualification are independent of theskill of the operator, in contrast to the present methods of the art,which are technically demanding and require a high level of skill andexperience.

The method presented herein allows a simultaneous calibration andqualification of a point cloud generator within 5 minutes of thegeneration of the cloud point. The method presented herein allows asimultaneous calibration and qualification of a point cloud generatorwithin 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 70, 80, 90, 100, 120,140, 160, 180, 200, 250, 300, 350, 400, 450, or 500 minutes of thegeneration of the cloud point. The speed of the method is achievedbecause no manual interventions are required; the method is automatic.

The method presented herein allows a simultaneous calibration andqualification of a point cloud generator without manual intervention,once the first scan has been instructed. in contrast to the presentmethods of the art, which requires extensive manual interventions andskill to adjust components of the point cloud generator.

In one embodiment of the invention, the following minimization algorithmis used, wherein Pr is the array of receiver data (size n), M is thecorresponding machine positions (size n), N is the array of controlpoints of the NURBS (size nc), and Q is the qualification matrix (size6).

void CalibrateAndQualify(in Pr, in M, out N, out Q) { // Initialization(set to zero) N = 0; Q = 0; C = 1e100; for iter = 1 to 10000 { //Perturb the current nurbs for i = 1 to nc Nnew(i) = N(i) + rand(−1,1);// Perturb the current orientation for i = 1 to 6 Qnew(i) = Q(i) +rand(−1,1); // Compute the 3D points for i = 1 to n P3(i) = Eval(Pr(i),Nnew, Qnew, M(i)); // Fit the points to the artifact Cnew = Fit(P3); //Update the best calibration/qualification so far if .(Cnew < C) { C =Cnew N = Nnew; Q = Qnew; } // Stop if necessary if (C < tol) return; } }////////////////////////////////////////////////////////////////////////// Point3D Eval(in Pr, in N, in Q, in M) // Nurbsevaluation see Piegi&Tiller P = N(Pr); // Orientation where Q is q 4×4matrix p = Q*p; // Machine position P = P + M; return P; }////////////////////////////////////////////////////////////////////////// double Fit(in P) { // Fit the artifact (here a sphere istaken as example); S = FitSphere(P, radius, center); // Compute the costC = 0; for i = 1 to n C = C + abs((center-P(i)){circumflex over( )}2-radius{circumflex over ( )}2); return C; }

The minimization algorithm uses a Monte-Carlo method where the currentcalibration and qualifications are randomly perturbed and accepted ifthe resulting set of points closer to the artifact (see Z. Michalewicz,“Modem Heuristics” for a survey of Monte-Carlo method). The calibrationis performed by means of a non-uniform rational B-spline (NURBS) curveor surface depending on the dimension of the receiver. The algorithmuses an order two NURBS with uniform knot vector (see Piegl and Tiller,“The NURBS Book”). The numbers of knots and control points depend on thedesired accuracy of the calibration. The qualification is defined as a4×4 matrix with 6 degrees of freedom.

In another embodiment, the present invention relates to the use of asingle artifact for performing the calibration and qualificationprocedure according to the method of the invention.

In another embodiment, the present invention relates to a computerprogram stored on a computer readable medium wherein the steps of themethod according to the invention are performed. Another embodiment ofthe invention concerns a computer adapted and programmed to carry outthe computer program according to the invention.

Moreover, the present invention also relates to a non-contact probeusable according to the method of the invention. This non-contact probeis consequently capable of performing at least 1 and preferably the 2steps of calibration and qualification in a single operation. Afterthese steps have been performed the non-contact probe is ready forindustrial use by the end-user, until it is dismounted from thelocalizer or until its position or orientation is changed with respectto the localizer.

The present invention also provides for a non-contact device comprisinga non-contact probe according to the invention, which is mounted on alocalizer, and an artifact.

1. A method of simultaneous calibration and qualification of a pointcloud generator, said point cloud generator comprising a non-contactprobe and a localizer, the method comprising: determining thetransformation of an electrical reading of the receivers in saidnon-contact probe in point coordinates relative to a coordinate systemfixed to the said probe and; and determining the orientation of the saidnon-contact probe in the measuring volume of the said localizer, whereinthe method uses a single artifact.
 2. The method according to claim 1,wherein said artifact is a physical object susceptible to point cloudgeneration, whose outer shape and/or part thereof is definable using amathematical function and/or look-up tables.
 3. The method according toclaim 2, wherein said artifact is a sphere, cylinder or box.
 4. Themethod according to claim 2, wherein said artifact is a sphere ofunknown diameter.
 5. The method according to claim 2, wherein saidartifact has unknown dimensions prior to the execution of said method.6. The method according to claim 2, wherein said artifact has unknownposition with respect to said localizer prior to the execution of saidmethod.
 7. The method according to claim 1, wherein said method isperformed without manual intervention.
 8. The method according to claim1, wherein said method is executed at a user's site.
 9. The method ofclaim 1, further comprising using the same device to both calibrate thepoint cloud generator and measure a physical object.
 10. The method ofclaim 1, wherein the calibration is performed within a coordinate systemfixed to the non-contact probe and without reference to points in knownpositions.
 11. A method of calibration only, or simultaneouslycalibration and qualification of a point cloud generator, said pointcloud generator comprising a non-contact probe and a localizer, themethod comprising: determining the transformation of an electricalreading of the receivers in said non-contact probe in point coordinatesrelative to the said probe; if simultaneously calibrating andqualifying, also determining the orientation of the said non-contactprobe in the measuring volume of the said localizer, either method usinga single artifact, wherein said artifact is a physical objectsusceptible to point cloud generation, whose outer shape and/or partthereof is definable using a mathematical function and/or look-uptables; a) scanning said artifact using said point cloud generator; b)calculating cloud points, P, using parameters relating to calibrationand qualification; c) calculating the position and optionally theorientation and/or size of said artifact using P calculated in b) andknowledge of the artifact according to a mathematical function and/orlook-up tables which define said artifact; d) comparing the values of P,with those calculated for the artifact derived from c); e) adjustingparameters relating to calibration and qualification; and f) repeatingb) to e) until parameters relating to calibration and qualification areobtained which provides the closest comparison according to step d). 12.The method according to claim 11, wherein b) is based on the genericcloud point function P=Q(f(Pr))+m(Pr) wherein Pr is a reading of areceiver of the non-contact probe; P is a cloud point, calculated fromPr, relative to a fixed coordinate system; f is a general mappingfunction, that maps receiver readings to 1D, 2D or 3D point coordinates,relative to a coordinate frame fixed to the non-contact probe; and Q isthe orientation of the non-contact probe and m(Pr) is the position ofsaid probe for a given value of Pr, both values with respect to a fixedcoordinate frame, none or either values considered as known and fixedparameters.
 13. The method according to claim 12, wherein f is anon-uniform rational B-spline function.
 14. The method according toclaim 11, wherein b) to f) comprise: b) calculating points according tothe generic cloud point function, said function re-expressed as: P=F(Pr, S)  wherein Pr is a reading of a receiver of the non-contactprobe;  P is a point, calculated from Pr, relative to a fixed coordinatesystem;  F is a compensation function based on f, Q and m(Pr), saidcompensation function being applied to Pr using parameter set S; c)calculating the position and optionally the orientation and/or size ofsaid artifact using values of P obtained in b); d) comparing the valuesof P, with those calculated for the artifact derived from c); e)adjusting S; and f) repeating b) to e) until a value of S is obtainedwhich provides the closest comparison according to d).
 15. The methodaccording to claim 11 wherein the values calculated for the artifact asmentioned in d) are derived from a mathematical function and/or look-uptables which define said artifact, the values corresponding to theposition, and if calculated orientation and/or size as obtained in c).16. The method according to claim 11 wherein c) comprises: g) comparingthe points P obtained in b) to those expected of said artifact accordingto a mathematical function and/or look-up tables which define saidartifact; h) adjusting one or more of the values corresponding to theposition and optionally the orientation and/or size of said artifact;and i) repeating g) and h) until values corresponding to the position,and if calculated orientation and/or size are obtained which provide theclosest comparison according to g).
 17. The method according to claim11, wherein the comparison performed in d) comprises one or more averagesquare distance, variance, volume, area, and/or axis of inertiacalculations.
 18. The method according to claim 9, wherein thecomparison performed in d) comprises one or more average squaredistance, variance, volume, area and/or axis of inertia calculations.19. A method of simultaneous calibration and qualification of a pointcloud generator, said point cloud generator comprising a two-dimensionalline laser scanner mounted on a 3D co-ordinate measuring machine, themethod comprising: a) scanning a sphere using said point cloudgenerator; b) calculating points according to the point functionP=F(Pr, S)  wherein Pr is a reading of a receiver of the two-dimensionalline laser scanner,  P is a point, calculated from Pr, relative to afixed coordinate system,  F is a compensation function based on f, Q andm or m(Pr), said compensation function being applied to Pr usingparameter set S,  Q is the orientation of the non-contact probe; m(Pr)is the position of said probe for a given value of Pr, both values withrespect to a fixed coordinate frame and none, either or both valuesconsidered as known parameters; c) comparing the points P obtained in b)to those expected of said sphere according to a mathematical functiondefining said sphere; d) adjusting one or more of the valuescorresponding to the position and size of said sphere; e) repeating c)and d) until values corresponding to the position and size are obtainedwhich provide the closest comparison according to step c); f) comparingthe values of P, with those calculated for the sphere, the latterobtained from mathematical function which defines said sphere, and thevalues corresponding to its position and size as obtained in step e); g)adjusting S; h) repeating b) to e) until value of S is obtained whichprovides the closest comparison according to f).
 20. A method to allowan unskilled operator to perform a simultaneous calibration andqualification of a point cloud generator, wherein the point cloudgenerator comprises a non-contact probe and a localizer, the methodcomprising: determining the transformation of an electrical reading ofthe receivers in said non-contact probe in point coordinates relative toa coordinate system fixed to the said probe; and determining theorientation of the said non-contact probe in the measuring volume of thesaid localizer, wherein the method uses a single artifact.
 21. A methodof performing calibration and qualification simultaneously of a pointcloud generator within about 5 minutes of generating the cloud point,wherein the point cloud generator comprises a non-contact probe and alocalizer, the method comprising: determining the transformation of anelectrical reading of the receivers in said non-contact probe in pointcoordinates relative to a coordinate system fixed to the said probe; anddetermining the orientation of the said non-contact probe in themeasuring volume of the said localizer, wherein the method uses a singleartifact.
 22. A method of performing simultaneous calibration andqualification of a point cloud generator without manual intervention,wherein the point cloud generator comprises a non-contact probe and alocalizer, the method comprising: determining the transformation of anelectrical reading of the receivers in said non-contact probe in pointcoordinates relative to a coordinate system fixed to the said probe; anddetermining the orientation of the said non-contact probe in themeasuring volume of the said localizer, wherein the method uses a singleartifact.
 23. Use of a single artifact for performing simultaneouscalibration and qualification of a point cloud generator, wherein thepoint cloud generator comprises a non-contact probe and a localizer, andwherein the calibration only or calibration and qualification areperformed according to the method comprising: determining thetransformation of an electrical reading of the receivers in saidnon-contact probe in point coordinates relative to a coordinate systemfixed to the said probe; and determining the orientation of the saidnon-contact probe in the measuring volume of the said localizer, whereinthe method uses a single artifact.
 24. A computer readable medium havinga computer program performing a method of simultaneous calibration andqualification of a point cloud generator comprising a non-contact probeand a localizer, wherein the method comprises: determining thetransformation of an electrical reading of the receivers in saidnon-contact probe in point coordinates relative to a coordinate systemfixed to the said probe; and determining the orientation of the saidnon-contact probe in the measuring volume of the said localizer, whereinthe method uses a single artifact.
 25. A computer programmed to executea computer readable medium having a computer program performing a methodof simultaneous calibration and qualification of a point cloud generatorcomprising a non-contact probe and a localizer, the method comprising:determining the transformation of an electrical reading of the receiversin said non-contact probe in point coordinates relative to a coordinatesystem fixed to the said probe; and determining the orientation of thesaid non-contact probe in the measuring volume of the said localizer,wherein the method uses a single artifact.
 26. A non-contact probeusable according to a method of simultaneous calibration andqualification of a point cloud generator comprising the non-contactprobe and a localizer, the method comprising: determining thetransformation of an electrical reading of the receivers in saidnon-contact probe in point coordinates relative to a coordinate systemfixed to the said probe; and determining the orientation of the saidnon-contact probe in the measuring volume of the said localizer, whereinthe method uses a single artifact.
 27. A non-contact device comprisingan artifact and a non-contact probe mounted on a localizer, wherein thenon-contact probe is usable according to the method comprising:simultaneous calibrating and qualifying, the non-contact device, whereincalibrating only or calibrating and qualifying comprises: determiningthe transformation of an electrical reading of the receivers in saidnon-contact probe in point coordinates relative to a coordinate systemfixed to the said probe; and determining the orientation of the saidnon-contact probe in the measuring volume of the said localizer, whereinthe method uses a single artifact.
 28. A method of calibration only of apoint cloud generator, said point cloud generator comprising anon-contact probe and a localizer, the method comprising: determiningthe transformation of an electrical reading of the receivers in saidnon-contact probe in point coordinates relative to a coordinate systemfixed to the said probe using a single artifact.
 29. The method of claim28, further comprising simultaneously qualifying the non-contact probewith said calibration, wherein the method further comprises determiningthe orientation of the said non-contact probe in the measuring volume ofthe said localizer.
 30. The method according to claim 28, wherein saidartifact is a physical object susceptible to point cloud generation,whose outer shape and/or part thereof is definable using a mathematicalfunction and/or look-up tables.
 31. The method according to claim 30,wherein said artifact is a sphere of unknown diameter.
 32. The methodaccording to claim 30, wherein said artifact has unknown dimensionsprior to performing said method.
 33. The method according to claim 30,wherein said artifact has unknown position with respect to saidlocalizer prior to performing said method.
 34. The method according toclaim 30, wherein said artifact is a sphere, cylinder or box.
 35. Themethod according to claim 28, wherein said method is performed withoutmanual intervention.
 36. The method according to claim 28, wherein saidmethod is performed at a user's site.
 37. The method of claim 28,further comprising using the same device to both calibrate the pointcloud generator and measure a physical object.
 38. The method of claim28, wherein the calibration is performed within a coordinate systemfixed to the non-contact probe and without reference to points in knownpositions.
 39. A method to allow an unskilled operator to perform acalibration of a point cloud generator, wherein the point cloudgenerator comprises a non-contact probe and a localizer, the methodcomprising: determining the transformation of an electrical reading ofthe receivers in said non-contact probe in point coordinates relative toa coordinate system fixed to the said probe, wherein the method uses asingle artifact.
 40. A method of performing a calibration of a pointcloud generator within about five minutes of generating the cloud point,wherein the point cloud generator comprises a non-contact probe and alocalizer, the method comprising: determining the transformation of anelectrical reading of the receivers in said non-contact probe in pointcoordinates relative to a coordinate system fixed to the said probe,wherein the method uses a single artifact.
 41. A method of performing acalibration of a point cloud generator without manual intervention,wherein the point cloud generator comprises a non-contact probe and alocalizer, the method comprising: determining the transformation of anelectrical reading of the receivers in said non-contact probe in pointcoordinates relative to a coordinate system fixed to the said probe,wherein the method uses a single artifact.
 42. Use of a single artifactfor performing the calibration of a point cloud generator, wherein thepoint cloud generator comprises a non-contact probe and a localizer, andwherein the calibration is performed according to the method comprising:determining the transformation of an electrical reading of the receiversin said non-contact probe in point coordinates relative to a coordinatesystem fixed to the said probe, wherein the method uses a singleartifact.
 43. A computer readable medium having a computer programperforming a method of calibration of a point cloud generator comprisinga non-contact probe and a localizer, wherein the method comprises:determining the transformation of an electrical reading of the receiversin said non-contact probe in point coordinates relative to a coordinatesystem fixed to the said probe, wherein the method uses a singleartifact.
 44. A computer programmed to execute a computer readablemedium having a computer program performing a method of calibration of apoint cloud generator comprising a non-contact probe and a localizer,the method comprising: determining the transformation of an electricalreading of the receivers in said non-contact probe in point coordinatesrelative to a coordinate system fixed to the said probe, wherein themethod uses a single artifact.
 45. A non-contact probe usable accordingto a method of calibration of a point cloud generator comprising thenon-contact probe and a localizer, the method comprising: determiningthe transformation of an electrical reading of the receivers in saidnon-contact probe in point coordinates relative to a coordinate systemfixed to the said probe, wherein the method uses a single artifact. 46.A non-contact device comprising an artifact and a non-contact probemounted on a localizer, wherein the non-contact probe is usableaccording to the method comprising: calibrating the non-contact device,wherein calibrating comprises: determining the transformation of anelectrical reading of the receivers in said non-contact probe in pointcoordinates relative to a coordinate system fixed to the said probe,wherein the method uses a single artifact.